Fears were raised after 25 people were killed and more than 100 wounded as bombs went off recently across New Delhi, one of the venues for the four-Test series starting in Bangalore on October 9.
"We are keeping an eye on the situation," Ponting told reporters here.
"We are in constant touch with security people to know what they think of the situation. They are comfortable with the security provided to us and we are comfortable too.
"I must say we are happy with the arrangements."
Vice-captain Michael Clarke said they had full faith in the security being provided to the team.
"We have a security expert with us and he is doing his job. The team has full faith in our cricket board and the Australian Cricketers Association. We know they are taking the right decisions," said Clarke.
The Australians will meet an Indian Board President's team in a four-day practice match starting here on Thursday.
The Bangalore Test will be followed by back-to-back matches in Mohali, New Delhi and Nagpur.
Australia cancelled a scheduled Test tour of Pakistan in March due to security concerns and were also one of the teams that forced the Champions Trophy there to be delayed by a year.